Week 2 — Graph & Model Workshop · "Compute GDP Three Ways"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 2 — measuring an economy's output; real vs. nominal; the GDP deflator · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 2
Format: build Meadowland's GDP the expenditure-approach way in a spreadsheet (or Desmos for the arithmetic), then work a full two-good economy to separate real growth from inflation, complete a short scaffold, interpret the result in words, then catch the AI's mistakes.

This is the course's signature weekly component. Every instructional week has one workshop: you set up a model, solve it, and explain what it means. All tools are links to free external sites — nothing to buy or download.

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Part 1 — The Big Picture

Last week you built an economy's PPF. This week you build the number economists actually use to size an economy up: Gross Domestic Product. You'll compute GDP the same way real analysts do — adding up the four expenditure buckets (C + I + G + NX) — and then dig one layer deeper: is a rising GDP number showing genuine growth, or just rising prices? The GDP deflator answers that question, and today you'll build one from scratch out of nothing but quantities and prices. (Next week you'll use the very same real-vs-nominal habit on wages, when you meet the CPI and the inflation rate.)

The tool: 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login) — or any spreadsheet; either works well for organizing the tables below.

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Part 2 — The Guiding Question

If a whole economy's spending is sorted into four buckets, how do those buckets add up to one GDP number — and when GDP rises, how do you tell how much of that rise is more STUFF versus just higher PRICES?

The scenario. The fictional economy of Meadowland reports these expenditure figures for the year (in billions of dollars): C = 500, I = 200, G = 150, X = 100, M = 50. Separately, economists have also determined that Meadowland's real GDP (this year's output, valued at base-year prices) is 750. To see exactly why real and nominal can differ, you'll also build a tiny two-good economy (pizzas and coffees) across two years, by hand.

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Part 3 — Set Up the Model (in a spreadsheet or Desmos)

1. Build a small table with one column per expenditure component: C, I, G, X, M. Enter Meadowland's five reported values.
2. Add two computed columns: NX (= X − M) and GDP (= C + I + G + NX).
3. Build a second small table for the two-good economy, with rows for base year and Year 2, and columns for quantity and price of each good (pizzas, coffees). You'll compute nominal GDP, real GDP, and the deflator from this table in Part 4.

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Part 4 — Solve (complete this scaffold)

Fill in the blanks. Show the steps.

Meadowland — GDP via the expenditure approach:

Question	Your answer
(a) Net exports: NX = X − M = 100 − 50	______
(b) GDP = C + I + G + NX = 500 + 200 + 150 + ______	______
(c) Meadowland's nominal GDP is the value from (b); its real GDP is given as 750. Compute the GDP deflator: nominal ÷ real × 100	______

A tiny two-good economy — pizzas and coffees:

Base year: 40 pizzas @ $5 each + 100 coffees @ $1 each.
Year 2: 44 pizzas @ $6 each + 110 coffees @ $1.20 each.

Question	Your answer
(d) Base-year nominal GDP: 40×$5 + 100×$1	______
(e) Year-2 nominal GDP (Year-2 quantities at Year-2 prices): 44×$6 + 110×$1.20	______
(f) Year-2 real GDP (Year-2 quantities at BASE-YEAR prices): 44×$5 + 110×$1	______
(g) Year-2 GDP deflator: (e) ÷ (f) × 100	______
(h) Real growth rate: [(f) − (d)] ÷ (d) × 100	______
(i) Nominal growth rate: [(e) − (d)] ÷ (d) × 100	______

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Part 5 — Interpret in Words (this is the SLO-A skill)

In 2–3 sentences, explain what the GDP deflator number you computed in (g) actually means in plain English (not just the digits), and why the real growth rate in (h) and the nominal growth rate in (i) are so different even though they describe the same two-good economy. (Hint: one of these two growth rates is "contaminated" by something — which one, and by what?)

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Part 6 — Analysis Questions

1. Meadowland's GDP counts C, I, G, and NX — but NOT everything that happens in the economy. Name one transaction that would not count in this year's GDP (pick something other than the examples already used in lecture), and explain in one sentence why it's excluded.
2. A classmate says, "If nominal GDP went up, the economy must have produced more stuff." Using your Part 4 two-good numbers, explain in 2–3 sentences why this claim is not always true — point to the specific gap between (h) and (i) as your evidence.
3. Connect to policy: a country's finance minister wants to announce "the economy grew!" using whichever number — nominal or real growth — looks most impressive. In 2–3 sentences, explain why economists insist on reporting real GDP growth rather than nominal, and what could go wrong (for good-faith or bad-faith reasons) if a government only ever reported the nominal figure. (You are not being asked whether any real government has done this — just to explain the incentive and the risk fairly.)

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Part 7 — AI-Critique Moment (required — the BYOAI step)

Bring in your approved chatbot (Gemini, Claude, or ChatGPT) and be the economist who checks its work.

1. Paste this to the chatbot: "An economy has C=500, I=200, G=150, X=100, M=50 (all in billions). What is GDP? Separately, if nominal GDP is 900 and real GDP is 750, what is the GDP deflator?"
2. Audit every claim against your own work:
   - Did it correctly compute NX = X − M = 50 (not X + M, and not M − X)?
   - Did it get GDP = 900?
   - Did it compute the deflator as nominal ÷ real × 100 = 120 — or did it flip the formula (real ÷ nominal, which would wrongly give about 83.3)?
   - Did it call a deflator above 100 "prices rose since the base year" — not "the economy produced more," which is a different claim entirely?
3. Write 2–3 sentences naming what the AI got right and at least one thing you had to correct or watch. (If it got everything right, explain how you verified each claim — that's the skill.)

The habit all term: the tool drafts, you judge. A chatbot will confidently flip the deflator formula or blur "nominal rose" with "the economy grew" — catching it is the point.

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Part 8 — What to Submit

One document (or spreadsheet/text entry) with: your Part 4 scaffold (both tables, with the arithmetic), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. A screenshot of your spreadsheet or Desmos work is welcome but optional. Due Sun, Sep 13, 11:59 p.m. (50 points).

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Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (see the Week-2 verified-numbers check).

Meadowland — GDP via the expenditure approach:
- (a) NX = 100 − 50 = 50 (billion). ✓
- (b) GDP = 500 + 200 + 150 + 50 = 900 (billion). ✓
- (c) Deflator = 900 ÷ 750 × 100 = 120. ✓ (Prices are, on average, 20% above the base year.)

Two-good economy (pizzas and coffees):
- (d) 40×$5 + 100×$1 = $200 + $100 = $300. ✓
- (e) 44×$6 + 110×$1.20 = $264 + $132 = $396. ✓
- (f) 44×$5 + 110×$1 = $220 + $110 = $330. ✓
- (g) 396 ÷ 330 × 100 = 120. ✓
- (h) (330 − 300) ÷ 300 × 100 = 10% (real growth). ✓
- (i) (396 − 300) ÷ 300 × 100 = 32% (nominal growth). ✓
- Cross-check: (1 + 0.10)(1 + 0.20) = 1.32 = (1 + 0.32) ✓ — real growth compounded with inflation equals nominal growth.

• Part 5: the deflator of 120 means prices this period are, on average, 20% higher than in the base year. The real growth rate (10%) isolates the genuine increase in the QUANTITY of pizzas and coffees produced, holding prices fixed at base-year levels; the nominal growth rate (32%) mixes that same 10% quantity increase together with the roughly 20% average price increase, so it reads much bigger. The nominal number is "contaminated" by inflation — that's exactly why economists insist on real GDP for judging genuine output change.
• Part 6: (1) any reasonable excluded transaction earns credit if the reason category is right — e.g., a used textbook resold between students (already counted when new), a parent's unpaid childcare (no market transaction), a stock trade (financial, not production), a government unemployment check (a transfer, not a purchase). (2) Nominal GDP rose 32% (from (i)) while real GDP rose only 10% (from (h)) — most of that 32% is price increases, not more pizzas and coffees actually produced; nominal rising is consistent with little or even zero real growth if prices rose enough. (3) Economists report real GDP growth because it isolates genuine output change; a government reporting only the (bigger, more flattering) nominal figure could mislead the public about how much the economy actually produced, whether the misreporting is due to poor communication or a deliberate choice to look better — full credit for any answer that explains the incentive and risk fairly without asserting any real government has done this.
• Part 7: full credit for a specific catch — most commonly the AI inverting the deflator formula (computing real ÷ nominal instead of nominal ÷ real, which would give roughly 83.3 instead of 120), mishandling NX (adding M instead of subtracting it), or conflating "prices rose" with "the economy produced more."

Grading rubric — 50 points

Criterion	Full	Partial	None
Scaffold (Part 4) — both tables, all nine blanks (a–i) correct with arithmetic shown (20)	20	10–16	0–8
Interpretation (Part 5) — deflator meaning + why real and nominal growth differ, stated in words (10)	10	5–8	0–4
Analysis (Part 6) — a correctly-reasoned excluded transaction; nominal-vs-real growth gap explained with evidence; the real-vs-nominal reporting incentive/risk presented fairly (12)	12	6–10	0–5
AI-critique (Part 7) — names a specific thing checked/corrected in the AI's answer (8)	8	4–6	0–3

Quality gate (self-checked): quantitative gate — NX=50, GDP=900, deflator=120 (Meadowland); base $300, Yr-2 nominal $396, Yr-2 real $330, deflator=120, real growth=10%, nominal growth=32% (two-good economy) — all Python-re-verified ✓. Graph-logic check (analog for this non-curve week) — deflator formula always nominal ÷ real (never inverted); real GDP always priced at base-year prices (never current-year); "nominal rose" never conflated with "the economy produced more"; the counted-vs-not-counted category for every Part 6/7 item verified against the canon ✓. Quantitative gate: PASS. Graph-logic check: PASS.